Problem: The equation of a circle $C$ is $x^2+y^2+8x+10y+32 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2+8x) + (y^2+10y) = -32$ $(x^2+8x+16) + (y^2+10y+25) = -32 + 16 + 25$ $(x+4)^{2} + (y+5)^{2} = 9 = 3^2$ Thus, $(h, k) = (-4, -5)$ and $r = 3$.